EP 0 705 727 B1 has disclosed a fitting system of this kind with a first fitting, a second fitting and a transmission element between the two fittings. Each fitting has a shaft piece, the rotation of which unlocks the fitting. To adjust the inclination of a backrest, the shaft piece is rotated by means of a first operating element on the second fitting, and a first lever seated thereon in a torsionally rigid manner is pivoted. The first lever takes along a second lever, which is connected in a torsionally rigid manner to the transmission element. The pivoting second lever rotates the transmission element, which transmits the rotary motion to the shaft piece of the first fitting. Both fittings unlock. To allow the backrest to be pivoted freely, the second fitting is assigned a free-pivoting device, which is locked by means of a pivotable pawl. The pawl is opened by means of a second operating element, and the pawl pivots the second lever by means of a cable pull as it pivots open. The pivoting second lever rotates the transmission element, which transmits the rotary motion to the shaft piece of the first fitting. The first fitting unlocks, while the second fitting remains locked. By means of the fitting system described, memorization of the backrest inclination is achieved. When the backrest is pivoted freely and then pivoted back, the previously set backrest inclination is re-assumed.